Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 630 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 52 cu cm (b) 8 cu cm (c) 24 cu cm (d) 9 cu cm
2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
3. 3.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
4. 4.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
5. 5.A cuboid is 5 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 30 sq cm (b) 124 sq cm (c) 31 sq cm (d) 62 sq cm
6. 6.A cuboid is 8 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 18 cu cm (b) 202 cu cm (c) 24 cu cm (d) 168 cu cm
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
9. 9.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
11. 11.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 294 sq cm (c) 196 sq cm (d) 49 sq cm
12. 12.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
15. 15.A cuboid is 10 cm long, 7 cm wide and 4 cm high. What is its total surface area? (a) 138 sq cm (b) 280 sq cm (c) 276 sq cm (d) 552 sq cm
16. 16.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 21 sq cm (c) 84 sq cm (d) 42 sq cm
17. 17.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
18. 18.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
19. 19.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
20. 20.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 100 sq cm (c) 600 sq cm (d) 1000 sq cm
21. 21.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 112 sq cm (b) 224 sq cm (c) 56 sq cm (d) 60 sq cm
22. 22.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
23. 23.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 24 cu cm (c) 8 cu cm (d) 16 cu cm
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
25. 25.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
27. 27.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
28. 28.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
29. 29.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 184 sq cm (b) 92 sq cm (c) 160 sq cm (d) 368 sq cm
30. 30.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
31. 31.A cuboid is 8 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 272 sq cm (b) 96 sq cm (c) 136 sq cm (d) 68 sq cm
32. 32.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
34. 34.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 8 times (d) 4 times
35. 35.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
36. 36.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 104 sq cm (b) 208 sq cm (c) 52 sq cm (d) 60 sq cm
39. 39.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 40 sq cm (b) 160 sq cm (c) 48 sq cm (d) 80 sq cm
40. 40.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times

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